MAGNETIC METHODS 



195 



2. Effects of Surfaces BC and AC (Figure 5'd;.— The effects of sur- 

 faces BC and AC may be calculated as above. The vertical component of 

 the field BC is : 



i P 



h 



Fig. 86. — Sketch showing quantities which 

 enter into the calculation of the effect of 

 contact BC. 



AZo = 



n: 



(h-h) (d + 8) 



XI 



In this case, it is simpler to integTate first with respect to y. 

 C dy 2_ 



dxdy 



l{y-yiy+ (x -xry+(d + 8)2]'/=- (x - xi)^ + {d + 8)'- 



Hence 



d + 8 



AZ2-2(/2-/3)l |-^^_^^^;+^^ + g)2-, dx 

 /o 

 = 2(/.-/,)[tan-i=^]^" 



or 



AZ.=2(/.-/3)(f+ta„-'^) 



The effect due to surface AC at P is obtained in similar fashion by integra- 

 ting between ,v and oo ; this gives : 



AZ3=2(/.-/,)(f-ta„-^) 



Hence, the total vertical anomaly (vertical component of the field 

 due to induced magnetism) is: 



AZ = AZi + AZ. + AZs = 27rh + 2(h-h) {^- tan"! ^^\ 



+ 2(7.-/3) (i+tan-^) 

 or 



AZ = 2U ( i - tan- i^) + 2'^ ( i + 'an- ^) (83) 



